Three-dimensional synthetic turbulence constructed by spatially randomized fractal interpolation

Area of Science:

• Fluid Dynamics
• Computational Physics
• Applied Mathematics

Background:

• Turbulence modeling is crucial for understanding complex fluid flows.
• Generating realistic synthetic turbulence fields is computationally challenging.
• Existing methods often struggle to capture the full statistical richness of turbulent flows.

Purpose of the Study:

• To develop a novel algorithm for constructing three-dimensional synthetic turbulence.
• To ensure the synthetic turbulence statistically resembles fields from direct numerical simulations.
• To reproduce key dynamical structures observed in empirical turbulence.

Main Methods:

• A spatially randomized fractal interpolation algorithm is employed.
• Random position mapping and log-Poisson distributed stretching factors are used.
• A linear combination function and a theoretical energy spectrum model for turbulence are integrated.

Main Results:

• The synthetic turbulence field exhibits statistical properties similar to direct numerical simulation (DNS) fields.
• Probability distributions of velocity, gradients, and increments match DNS.
• Anomalous scaling behavior of velocity structure functions precisely follows the SL94 model.
• Local dynamical structures, like the Q-R plane teardrop shape, are reproduced after short DNS.

Conclusions:

• The fractal interpolation algorithm effectively generates high-fidelity synthetic turbulence.
• The method provides a promising alternative for turbulence simulation and research.
• The synthetic fields capture essential statistical and dynamical features of real turbulence.